right across what then was by far the most thickly populated and the most important part of the island.
A third section in all such rivers (and, from what we have said above, a short and insignificant one in the case of the Thames) may be called the head-waters of the river: where the stream is so shallow or so uncertain as to be no longer navigable. In the case of the Thames these head-waters cover no more than ten to fifteen miles of country. With the exception of rivers that run through mountain districts this section of a river's course is nearly always small in proportion to the rest; but the Thames, just as it has the longest proportion of navigable water, has also by far the shortest proportion of useless head-water of all the shorter European rivers.
There is a further discussion as to what is the true source of the Thames, and which streams may properly be regarded as its head-waters: the Churn, especially since the digging of the canal, having a larger flow than the stream from Thames head; but whichever is chosen, the non-navigable portion starts at the same point, and is the third of the divisions into which the valley ranges itself when it is considered in its length, as a highway from the west to the east of England. The two limits, then, are at London Bridge and at Cricklade, or rather at some point between Lechlade and Cricklade, and nearer to the latter.
But a river has a second topographical and historic function. It cannot only be considered longitudinally as a
